diff --git a/dynamic_programming/rod_cutting.py b/dynamic_programming/rod_cutting.py index 34350cb8202b..c3111dcfc8a1 100644 --- a/dynamic_programming/rod_cutting.py +++ b/dynamic_programming/rod_cutting.py @@ -1,58 +1,57 @@ -### PROBLEM ### -""" -We are given a rod of length n and we are given the array of prices, also of -length n. This array contains the price for selling a rod at a certain length. -For example, prices[5] shows the price we can sell a rod of length 5. -Generalising, prices[x] shows the price a rod of length x can be sold. -We are tasked to find the optimal solution to sell the given rod. -""" - -### SOLUTION ### -""" -Profit(n) = max(1 m): - m = yesCut[i] - - solutions[n] = m - return m - - - -### EXAMPLE ### -length = 5 -#The first price, 0, is for when we have no rod. -prices = [0, 1, 3, 7, 9, 11, 13, 17, 21, 21, 30] -solutions = [-1 for x in range(length+1)] - -print(CutRod(length)) +from typing import List + +def rod_cutting(prices: List[int],length: int) -> int: + """ + Given a rod of length n and array of prices that indicate price at each length. + Determine the maximum value obtainable by cutting up the rod and selling the pieces + + >>> rod_cutting([1,5,8,9],4) + 10 + >>> rod_cutting([1,1,1],3) + 3 + >>> rod_cutting([1,2,3], -1) + Traceback (most recent call last): + ValueError: Given integer must be greater than 1, not -1 + >>> rod_cutting([1,2,3], 3.2) + Traceback (most recent call last): + TypeError: Must be int, not float + >>> rod_cutting([], 3) + Traceback (most recent call last): + AssertionError: prices list is shorted than length: 3 + + + + Args: + prices: list indicating price at each length, where prices[0] = 0 indicating rod of zero length has no value + length: length of rod + + Returns: + Maximum revenue attainable by cutting up the rod in any way. + """ + + prices.insert(0, 0) + if not isinstance(length, int): + raise TypeError('Must be int, not {0}'.format(type(length).__name__)) + if length < 0: + raise ValueError('Given integer must be greater than 1, not {0}'.format(length)) + assert len(prices) - 1 >= length, "prices list is shorted than length: {0}".format(length) + + return rod_cutting_recursive(prices, length) + +def rod_cutting_recursive(prices: List[int],length: int) -> int: + #base case + if length == 0: + return 0 + value = float('-inf') + for firstCutLocation in range(1,length+1): + value = max(value, prices[firstCutLocation]+rod_cutting_recursive(prices,length - firstCutLocation)) + return value + + +def main(): + assert rod_cutting([1,5,8,9,10,17,17,20,24,30],10) == 30 + # print(rod_cutting([],0)) + +if __name__ == '__main__': + main() +